I have a 2005 3500 SRW, so my advice is based on that. You can click the link in my sig to see what all I have done to the suspension, but basically it's what I am recommending. I will hit over 7K lbs on the rear axle many weekends this time of year.
My 3500 is identical to your 2500 in terms of frame/brakes/suspension/etc with the one exception you noted.. the upper overload springs. IMHO they are not needed on a SRW truck as they really aren't engaged until you are at 95%, or higher, or the tire loading with OEM tires. If you do upgrade the wheels tires to go well above 6K on the rear axle they are nice, but still let the rear sag too much IMHO without stable loads (I want a set for summer use).
You need to determine how much pin weight you are going to have. The recommended amount it 15-25%, or 3,600 to 6,000lbs of additional rear axle weight. The amount of weight that will hit the front axle it negligible.
First things first, do you have the wheels/tires to support an additional 3,600 to 6,000lbs on the rear axle? If you have OEM wheels and tires the answer is NO. 19.5's are really your only option to support that much weight safely as a SRW, or a DRW. You didn't list or state your cab/bed configuration, but plan on at least 3,000lbs of "empty" rear axle weight. You need wheels/tires that will support up to 9,000lbs on the rear axle or 4,500lbs a corner. DRW or 19.5 245/70R19.5 in LRG.. your only 2 options.
Now for suspension. The suspension will handle the weight fairly well but I would make a few upgrades.
1) If you have a front level kit remove it, or go to a 1" at most.
2) Exhaust Brake
3) Good Brake controller, at a minimum a proportional one.
4) Shocks, Bilstein 5100's are a great shock for a heavy load.
5) Rear anti-sway bar. I like the standard Hellwig for non-TC applications, it makes a HUGE difference
6) Airbags and a compressor.
You will be above the highest GVWR that frame ever had, 12,200, so be aware that while the frame/suspension may be fine you are above the design weight of the brakes. The trailer should stop itself, but make sure the trailer brakes are always in top working order.
You might also find that the BD runs hotter than you want when towing heavy, so consider a Smarty. Ditch that POS K&N, or the high airflow needed for a 30K+ GCW will eat your turbo quickly.